More than 700 people have signed a petition on Change.org claiming the cathedral would be offensive to host the play.
The petition states: "Ricardians (those who believe Richard was wrongly accused of usurping the crown by murdering his way to it, but that he was actually one of our most just and enlightened kings) are clearly aware that Shakespeare's play was fiction and probably written as a satire on the corruption of power, but members of the general public often believe that Shakespeare was accurate, so each time the play is produced it only adds to the unfair reputation that Richard has been given.
"That is bad enough, but for Leicester Cathedral to actually put on this play in the very place where his earthly remains are interred is tantamount to sacrilege.
"The Cathedral undertook to treat the last English king to die in battle with 'dignity and honour', so how can these performances (of the very play which does the most to reinforce the unjust reputation he suffers from) be reconciled with this promise?
"We the undersigned find it offensive and inappropriate that Leicester Cathedral are allowing Shakespeare's biased version of Richard to be performed in the place where his mortal remains are supposedly at rest."
Protesters urged the cathedral to cancel the performances, and refuse all future performances of the play.
In response to the backlash, Leicester Cathedral said it aims to expand its cultural work and the upcoming production will one of a few performances it has hosted in recent years.
The church also hosted Shakespeare's Richard III in 2014.
In a statement, the church acknowledged different beliefs held about Richard III: "Research by the Richard III Society with others has revealed new historical aspects which have reshaped understanding.
"Investigation by the University of Leicester, working with the Looking for Richard Project, has provided further scientific insights. Shakespeare's play will remain significant as a core work within the canon of English drama.
"The Cathedral enables many to engage with different dimensions of this complex story. This helps us to make sense of our understandings of monarchy, disability, power, faith, science, the arts, history, fact and fiction.
"The legacy of the myths, the mystery and the man himself will continue to interplay and at times this will arouse strong responses."
The cathedral promised the upcoming performances on 19th and 20th July will be memorable and committed to "ensure new generations keep encountering his legacy."
The dark comic drama will also be staged at Ely, Peterborough, Gloucester, Bristol and Salisbury Cathedrals, as well as London's Temple Church.
